On an inverting amplifier (when the inverting input is used for feedback), current flowing into the input gathers at the input pin because of its high impedance (net resistance). This causes the output pin to go negative to such a degree that the current pulled though the feedback line equals that at on the input line.

Think of a T-junction, and all the cars are travelling in one direction, taking one of the two roads available only. The cars are coming from your current source, and are driving towards the feedback line. The reason for this is the great big wall stuck in the middle of the other road.

This 'other road' is the input pin of the Op-Amp, and with no current, V=0*R=0 (zero Volts).